CS 445 / 645 Introduction to Computer Graphics

1. CS 445 / 645Introduction to Computer Graphics Lecture 15 Lighting

2. Beier & Neely Morphing • Key point: • Cross dissolve by itself fails when features are not aligned • Intermediate blend of two faces may appear to have four eyes • Warping an image slides pixels around so that features can be located someplace specific • Warping one face image to align with another before cross dissolve eliminates problem of four eyes

3. Beier & Neely Example Image0 Warp0 Result Image1 Warp1

4. Beier & Neeley Example Image0 Warp0 Result Image1 Warp1

5. Image Morphing • The warping step is the hard one • Aim to align features in images H&B Figure 16.9

6. Mapping p v u p’ Feature-Based Warping • Beier & Neeley use pairs of lines to specify warp • Given p in dst image, where is p’ in source image? v u’ Source image Destination image u is a fraction Why not the sameunits? v is a length (in pixels)

7. Unique element of paper

8. Illumination • How do we compute radiance for a sample ray? Angel Figure 6.2

9. Goal • Must derive computer models for ... • Emission at light sources • Scattering at surfaces • Reception at the camera • Desirable features … • Concise • Efficient to compute • “Accurate”

10. Overview • Direct (Local) Illumination • Emission at light sources • Scattering at surfaces • Global illumination • Shadows • Refractions • Inter-object reflections Direct Illumination

11. Modeling Light Sources • IL(x,y,z,q,f,l) ... • describes the intensity of energy, • leaving a light source, … • arriving at location(x,y,z), ... • from direction (q,f), ... • with wavelength l (x,y,z) Light

12. Empirical Models • Ideally measure irradiant energy for “all” situations • Too much storage • Difficult in practice l

13. Ambient Light Sources • Objects not directly lit are typically still visible • e.g., the ceiling in this room, undersides of desks • This is the result of indirect illuminationfrom emitters, bouncing off intermediate surfaces • Too expensive to calculate (in real time), so we use a hack called an ambient light source • No spatial or directional characteristics; illuminates all surfaces equally • Amount reflected depends on surface properties

14. Ambient Light Sources • For each sampled wavelength (R, G, B), the ambient light reflected from a surface depends on • The surface properties,kambient • The intensity, Iambient,of the ambient light source (constant for all points on all surfaces ) • Ireflected = kambient Iambient

15. Ambient Light Sources • A scene lit only with an ambient light source: Light PositionNot Important Viewer PositionNot Important Surface AngleNot Important

16. Ambient Term • Represents reflection of all indirect illumination This is a total hack (avoids complexity of global illumination)!

17. Directional Light Sources • For a directional light source we make simplifying assumptions • Direction is constant for all surfaces in the scene • All rays of light from the source are parallel • As if the source were infinitely far away from the surfaces in the scene • A good approximation to sunlight • The direction from a surface to the light source is important in lighting the surface

18. Directional Light Sources • The same scene lit with a directional and an ambient light source

19. Point Light Sources • A point light source emits light equally in all directions from a single point • The direction to the light from a point on a surface thus differs for different points: • So we need to calculate a normalized vector to the light source for every point we light: l p

20. Other Light Sources • Spotlights are point sources whose intensity falls off directionally. • Requires color, pointdirection, falloffparameters • Supported by OpenGL

21. Other Light Sources • Area light sources define a 2-D emissive surface (usually a disc or polygon) • Good example: fluorescent light panels • Capable of generating soft shadows (why?)

22. Overview • Direct (Local) Illumination • Emission at light sources • Scattering at surfaces • Global illumination • Shadows • Refractions • Inter-object reflections Direct Illumination

23. Modeling Surface Reflectance • Rs(q,f,g,y,l) ... • describes the amount of incident energy, • arriving from direction (q,f), ... • leaving in direction (g,y), … • with wavelength l l (q,f) (y,l) Surface

24. Empirical Models • Ideally measure radiant energy for “all” combinations of incident angles • Too much storage • Difficult in practice l (q,f) (y,l) Surface

25. The Physics of Reflection • Ideal diffuse reflection • An ideal diffuse reflector, at the microscopic level, is a very rough surface (real-world example: chalk) • Because of these microscopic variations, an incoming ray of light is equally likely to be reflected in any direction over the hemisphere: • What does the reflected intensity depend on?

26. Diffuse Reflection • How much light is reflected? • Depends on angle of incident light q Surface

27. Diffuse Reflection • How much light is reflected? • Depends on angle of incident light dL q dA Surface

28. Lambert’s Cosine Law • Ideal diffuse surfaces reflect according to Lambert’s cosine law: The energy reflected by a small portion of a surface from a light source in a given direction is proportional to the cosine of the angle between that direction and the surface normal • These are often called Lambertian surfaces • Note that the reflected intensity is independent of the viewing direction, but does depend on the surface orientation with regard to the light source

29. Lambert’s Law

30. Computing Diffuse Reflection • The angle between the surface normal and the incoming light is the angle of incidence: • Idiffuse = kd Ilightcos  • In practice we use vector arithmetic: • Idiffuse = kd Ilight (n • l) l n 

31. Diffuse Lighting Examples • We need only consider angles from 0° to 90° (Why?) • A Lambertian sphere seen at several different lighting angles:

32. Specular Reflection • Shiny surfaces exhibit specular reflection • Polished metal • Glossy car finish • A light shining on a specular surface causes a bright spot known as a specular highlight • Where these highlights appear is a function of the viewer’s position, so specular reflectance is view dependent

33. The Physics of Reflection • At the microscopic level a specular reflecting surface is very smooth • Thus rays of light are likely to bounce off the microgeometry in a mirror-like fashion • The smoother the surface, the closer it becomes to a perfect mirror

34. The Optics of Reflection • Reflection follows Snell’s Laws: • The incoming ray and reflected ray lie in a plane with the surface normal • The angle that the reflected ray forms with the surface normal equals the angle formed by the incoming ray and the surface normal: (l)ight = (r)eflection

35. Specular Reflection • Reflection is strongest near mirror angle • Examples: mirrors, metals N R q q L

36. Geometry of Reflection N RN(L) L qL qR qL=qR

37. Geometry of Reflection N (N.L)N RN(L) L cos(qi)N qL qR qL=qR

38. Geometry of Reflection 2(N.L)N N RN(L) L qL qR qL=qR

39. Geometry of Reflection 2(N.L)N L N RN(L) L q qL q qR qL=qR

40. Geometry of Reflection 2(N.L)N L N RN(L) L qL qR qL=qR

41. Non-Ideal Specular Reflectance • Snell’s law applies to perfect mirror-like surfaces, but aside from mirrors (and chrome) few surfaces exhibit perfect specularity • How can we capture the “softer” reflections of surface that are glossy rather than mirror-like? • One option: model the microgeometry of the surface and explicitly bounce rays off of it • Or…

42. Non-Ideal Specular Reflectance: An Empirical Approximation • Hypothesis:most light reflects according to Snell’s Law • But because of microscopic surface variations, some light may be reflected in a direction slightly off the ideal reflected ray • Hypothesis:as we move from the ideal reflected ray, some light is still reflected

43. Non-Ideal Specular Reflectance: An Empirical Approximation • An illustration of this angular falloff: • How might we model this falloff?

44. Phong Lighting • The most common lighting model in computer graphics was suggested by Phong: v • The nshinyterm is a purelyempirical constant that varies the rate of falloff • Though this model has no physical basis, it works (sort of) in practice

45. Phong Lighting: The nshinyTerm • This diagram shows how the Phong reflectance term drops off with divergence of the viewing angle from the ideal reflected ray: • What does this term control, visually? Viewing angle – reflected angle

46. Calculating Phong Lighting • The cos term of Phong lighting can be computed using vector arithmetic: • v is the unit vector towards the viewer • ris the ideal reflectance direction v

47. Phong Examples • These spheres illustrate the Phong model as l and nshiny are varied:

48. Combining Everything • Simple analytic model: • diffuse reflection + • specular reflection + • emission + • “ambient” Surface

49. Surface Combining Everything • Simple analytic model: • diffuse reflection + • specular reflection + • emission + • “ambient”

50. OpenGL Reflectance Model • Sum diffuse, specular, emission, and ambient